30 ideas
| 1848 | We are coerced into assent to a truth by reason's violence [Aquinas] |
| Full Idea: We are coerced into assent to a truth by reason's violence. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.10) |
| 1858 | The mind is compelled by necessary truths, but not by contingent truths [Aquinas] |
| Full Idea: Mind is compelled by necessary truths that can't be regarded as false, but not by contingent ones that might be false. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 12) |
| 21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
| Full Idea: The ban on 'impredicative' definitions says you can't define a class in terms of a totality to which that class must be seen as belonging. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: So that would be defining 'citizen' in terms of the community to which the citizen belongs? If you are asked to define 'community' and 'citizen' together, where do you start? But how else can it be done? Russell's Reducibility aimed to block this. |
| 1852 | For the mind Good is one truth among many, and Truth is one good among many [Aquinas] |
| Full Idea: Good itself as taken in by mind is one truth among others, and truth itself as goal of mind's activity is one good among others. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) |
| 21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
| Full Idea: The Axiom of Reducibility avoids impredicativity, by asserting that for any predicate of given arguments defined by quantifying over higher-order functions or classes, there is another co-extensive but predicative function of the same type of arguments. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Eventually the axiom seemed too arbitrary, and was dropped. Linsky's book explores it. |
| 21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
| Full Idea: The theory of definite descriptions may eliminate apparent commitment to such entities as the present King of France, but certainly not to the present Queen of England. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.3) |
| 21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
| Full Idea: With the principle of extensionality anything true of one propositional functions will be true of every coextensive one. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.3) |
| 21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
| Full Idea: The problem for logicism was to find definitions of the primitive notions of Peano's theory, number, successor and 0, in terms of logical notions, so that the postulates could then be derived by logic alone. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7) | |
| A reaction: Both Frege and Russell defined numbers as equivalence classes. Successor is easily defined (in various ways) in set theory. An impossible set can exemplify zero. The trouble for logicism is this all relies on sets. |
| 21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
| Full Idea: The higher types are needed for intensional phenomena, cases where the same class is picked out by distinct propositional functions. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.4) | |
| A reaction: I take it that in this way 'x is renate' can be distinguished from 'x is cordate', a task nowadays performed by possible worlds. |
| 21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
| Full Idea: The types is 'ramified' because there are further differences between the type of a function defined in terms of a quantifier ranging over other functions and the type of those other functions, despite the functions applying to the same simple type. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Not sure I understand this, but it evidently created difficulties for dealing with actual mathematics, and Ramsey showed how you could manage without the ramifications. |
| 21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
| Full Idea: The original ramified theory of types ...furthern subdivides each of the types of the 'simple' theory according to the range of the bound variables used in the definition of each propositional function. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: For a non-intiate like me it certainly sounds disappointing that such a bold and neat theory because a tangle of complications. Ramsey and Russell in the 1920s seem to have dropped the ramifications. |
| 21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
| Full Idea: It is often thought that Logicism was a failure, because after Frege's contradiction, Russell required obviously nonlogical principles, in order to develop mathematics. The axioms of Reducibility, Infinity and Choice are cited. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: Infinity and Choice remain as axioms of the standard ZFC system of set theory, which is why set theory is always assumed to be 'up to its neck' in ontological commitments. Linsky argues that Russell saw ontology in logic. |
| 21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
| Full Idea: ZF set theory is seen as a rival to logicism as a foundational scheme. Set theory is for those who have given up the project of reducing mathematics to logic. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.1) | |
| A reaction: Presumably there are other rivals. Set theory has lots of ontological commitments. One could start at the other end, and investigate the basic ontological commitments of arithmetic. I have no idea what those might be. |
| 21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
| Full Idea: Rather than directly constructing properties as sets of objects and proving neat facts about properties by proxy, we can assert biconditionals, such as that an object has a property if and only if it is in a certain set. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.6) | |
| A reaction: Linsky is describing Russell's method of logical construction. I'm not clear what is gained by this move, but at least it is a variant of the usual irritating expression of properties as sets of objects. |
| 1860 | Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas] |
| Full Idea: All our knowledge comes through our senses, but that doesn't mean that everything we know is sensed. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 18) |
| 1855 | If we saw something as totally and utterly good, we would be compelled to will it [Aquinas] |
| Full Idea: Something apprehended to be good and appropriate in any and every circumstance that could be thought of would compel us to will it. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) |
| 1856 | Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas] |
| Full Idea: Nothing can be willed except good, but many and various things are good, and you can't conclude from this that wills are compelled to choose this or that one. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 05) |
| 1862 | However habituated you are, given time to ponder you can go against a habit [Aquinas] |
| Full Idea: However habituated you are, given time to ponder you can go against a habit. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 24) |
| 1849 | Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas] |
| Full Idea: Reasoning powers can entertain opposite objects. Now will is a reasoning power, so will can entertain opposites and is not compelled to embrace one of them. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.x2) |
| 1861 | The will is not compelled to move, even if pleasant things are set before it [Aquinas] |
| Full Idea: The will is not compelled to move, for it doesn't have to want the pleasant things set before it. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 21) |
| 1853 | Because the will moves by examining alternatives, it doesn't compel itself to will [Aquinas] |
| Full Idea: Because will moves itself by deliberation - a kind of investigation which doesn't prove some one way correct but examines the alternatives - will doesn't compel itself to will. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) |
| 1854 | We must admit that when the will is not willing something, the first movement to will must come from outside the will [Aquinas] |
| Full Idea: We are forced to admit that, in any will that is not always willing, the very first movement to will must come from outside, stimulating the will to start willing. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) | |
| A reaction: cf Nietzsche |
| 1847 | The will must aim at happiness, but can choose the means [Aquinas] |
| Full Idea: The will is compelled by its ultimate goal (to achieve happiness), but not by the means to achieve it. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.07) |
| 1857 | We don't have to will even perfect good, because we can choose not to think of it [Aquinas] |
| Full Idea: The will can avoid actually willing something by avoiding thinking of it, since mental activity is subject to will. In this respect we aren't compelled to will even total happiness, which is the only perfect good. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 07) |
| 1846 | The will can only want what it thinks is good [Aquinas] |
| Full Idea: Will's object is what is good, and so it cannot will anything but what is good. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.06) |
| 1850 | Without free will not only is ethical action meaningless, but also planning, commanding, praising and blaming [Aquinas] |
| Full Idea: If we are not free to will in any way, but are compelled, everything that makes up ethics vanishes: pondering action, exhorting, commanding, punishing, praising, condemning. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) | |
| A reaction: If doesn't require some magical 'free will' to avoid compulsions. All that is needed is freedom to enact your own willing, rather than someone else's. |
| 1851 | Good applies to goals, just as truth applies to ideas in the mind [Aquinas] |
| Full Idea: Good applies to all goals, just as truth applies to all forms mind takes in. | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.reply) | |
| A reaction: In danger of being tautological, if good is understood as no more than the goal of actions. It seems perfectly possibly to pursue a wicked end, and perhaps feel guilty about it. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 1859 | Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas] |
| Full Idea: Even a sufficient cause doesn't always compel its effect, since it can sometimes be interfered with so that its effect doesn't happen | |
| From: Thomas Aquinas (Quaestiones Disputatae de Malo [1271], Q6.h to 15) |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |